Three people died on Tuesday when their car fell into a swollen river as torrential rain caused widespread flooding in Tuscany and Umbria.

The flooding in central Italy followed heavy rain and an unusually high tide in Venice – the sixth highest level since records began in 1872 – which left nearly three-quarters of the lagoon city under water.

The three people feared to have drowned – two men and a woman – were believed to be employees of Enel, Italy's biggest electricity company.

The car they were travelling in was swept off a collapsed bridge in Grosseto, a few miles inland from the Tuscan coast.

The deaths brought the death toll from the bad weather to four – on Monday a 73-year old man was swept away in his car by floodwaters near the town of Capalbio, also on the coast of Tuscany.

Elsewhere in the region, normally known for its sun-baked summers and idyllic landscapes, people were plucked from their roofs of their flooded homes by rescue helicopters.

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As rivers broke their banks, more than 100 people were forced to flee their homes and take refuge in emergency shelters.

The towns of Orbetello and Albinia were inundated with water, with the latter "looking like Venice", according to Italian news reports.

In Rome, the Tiber was so swollen that it was no longer possible to walk or cycle along its banks. Major roads and railway lines were blocked.

Enrico Rossi, the head of Tuscany's regional government, said the flooding was so severe that it required intervention by the army.

He said floods had worsened in recent years and blamed global warming.

"Climate change is causing ever more serious flooding," Mr Rossi told Corriere della Sera. "We can no longer postpone the work that needs to be done." He called for 50 million euros a year for the next 10 years to build new bridges and embankments.

The flooding in Venice on Sunday and Monday allowed tourists to pull on their swimming costumes and go take a dip in St Mark's Square, the lowest lying part of the city.

The level of the water reached 149 centimetres – the highest since 2008.

The flooding underlined the need for a multi-billion pound flood protection barrier to be completed as quickly as possible, the consortium behind the project said.

The Moses flood prevent project entails the construction of giant steel gates across the three inlets through which water from the Adriatic surges into Venice's lagoon.

The 300-tonne hinged panels will be fixed to massive concrete bases dug into the sea bed and will be raised whenever a dangerously high tide is predicted.

Inaugurated by Silvio Berlusconi, the then prime minister, in 2003, it was due to be completed this year but is now expected to be operational in 2016.

The consortium, the Consorzio Venezia Nuova, said that had the much-delayed project been up and running on Sunday, Venice would have remained dry.

"This high tide underlines the urgency and necessity of completing the project quickly," it said in a statement.